HI, welcome to GoY, if you look at the plant, you will see that there are a number of fan shaped pieces in the clump, to divide these, take a sharp clean knife, and place it in between fans, if you can about part way between, then cut cleanly straight down, you may be able to get 2, 3, or more from a large plant, I would just use ordinary potting compost, save your own compost for your flower beds, or veg beds, I wouldn't use ordinary garden soil unless it's a very well draining loam, Derek.

Agapanthus love to be pot bound and I always wait till the plant bursts the pot (this has happened twice) before I repot...and only then in a pot a little larger than the broken pot. I grow the agapanthus Northern Star and last year I had 28 large flower heads from a plant in a pot no larger than 12 inches in diameter. Years ago I did divide up a mature agapanthus and had to wait several years before I was rewarded with flowers again. My advice .....leave the plant alone unless you absolutely have to repot.

If they like to be pot bound in order to flower, how do they flower in the garden?

If very root bound then 2 garden forks and some muscle is called for. They actually do not like being pot bound - it only works in the UK as we have mild, long and wet winters. In the US where it is much drier then I would not let it get pot bound and feed well.